Mathematics
In the figure (i) given below, A, B, C and D are points on the circle with center O. Given that ∠ABC = 62°, find
(i) ∠ADC
(ii) ∠CAB
Circles
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Answer
(i) From figure,
⇒ ∠ADC = ∠ABC (Angles in same segment are equal)
⇒ ∠ADC = 62°.
Hence, ∠ADC = 62°.
(ii) We know that,
Angle in a semi-circle is a right angle.
∠ACB = 90°
Using angle sum property,
⇒ ∠CAB + ∠ACB + ∠ABC = 180°
⇒ ∠CAB + 90° + 62° = 180°
⇒ ∠CAB + 152° = 180°
⇒ ∠CAB = 180° - 152°
⇒ ∠CAB = 28°.
Hence, ∠CAB = 28°.
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